Three Brands of AAA Batteries Are Compared to See Which

question 782

Essay

Three brands of AAA batteries are compared to see which last longest. Each brand of
battery is tested in four different devices (a TV remote control, a hand-held game, a
miniature flashlight, and a digital camera). The experiment is run once for each
combination of brand and device. The twelve runs are ordered randomly. The time that the
each battery lasts (in minutes) under continuous usage is recorded. $$\begin{array} { | l | r | r | r | } \hline \text { Device } & \text { Brand A } & \text { Brand B } & \text { Brand C } \\\hline \text { Remote } & 1320 & 1220 & 1250 \\\hline \text { Game } & 480 & 460 & 450 \\\hline \text { Light } & 245 & 225 & 240 \\\hline \text { Camera } & 81 & 72 & 77 \\\hline\end{array}$$
The two-way ANOVA table for response variable Time and factors Brand and Device is
given below.
a. Write the model equation for this ANOVA. (Use symbols or words, no numbers.)
b. Test to see whether there is a brand effect. Write the hypotheses being tested, and state
your conclusion using a 5% level of significance. Write your conclusion in the context of
this problem.
c. Explain the role that the device factor plays in this analysis.
d. Can an interaction term be added to this model? Explain.
e. Use the plots below to check the ANOVA conditions.

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Definitions:

Tech-Savvy Audiences

Groups of people who are highly knowledgeable about and comfortable using advanced technology and digital platforms.

Flowchart

A diagrammatic representation used to illustrate a sequence of actions or steps in a complex system or process.

Decision Points

Critical moments within a process where a choice must be made that will affect the outcome.

Linear Regression

A statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.